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Barry Ruddick

Abstract

Thermohaline intrusions found in Meddy “Sharon” were laterally coherent The slope of these intrusions across density surfaces was in opposite senses in the upper and lower part of the meddy, consistent with (i) the McIntyre instability for Prandtl number less than one, in which case mass flux (assumed equal in heat and salt diffusivity) dominates over viscosity, or (ii) double-diffusive intrusions, in which diffusive fluxes dominate in the upper, diffusively unstable portion of the meddy, and finger fluxes dominate in the lower, fingering-unstable part. The magnitudes of the intrusion slopes are outside the range of angles for which the McIntyre mechanism can provide energy to the intrusive motions, but within the range of angles for which double-diffusive mixing can drive the intrusions. Thus, the energy source for the intrusions is not the kinetic or potential energy of the geostrophic shear flow, but is the potential energy associated with the lateral salinity and temperature gradients. Furthermore, the observed vertical wavelength of the intrusions is much closer to that predicted for double-diffusive intrusions than McIntyre. Thus, the intrusions are double-diffusively driven, and even a combined “triple-diffusive” instability may involve double-diffusive fluxes as the energy release mechanism.

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David Walsh and Barry Ruddick

Abstract

The influence of nonconstant diffusivity and viscosity on double-diffusive interleaving is examined using a simple model. The analysis allows a prediction of the slope, vertical wavenumber, and growth rate of the fastest-growing interleaving mode for specified background gradients of salinity and temperature. Allowing the salt diffusivity to be a function of the density ratio Rp leads to a larger growth rate and a lower vertical wavenumber than in the constant diffusivity case considered by Toole and Georgi, while the cross-front slope of the intrusions is essentially unaffected. The nonconstant viscosity included in the model formulation is found to have no effect on the form of the solutions. The larger vertical scales and growth rates predicted by the model can be traced to an enhanced “effective diffusivity” resulting from the diffusivity gradients associated with the growing intrusions. A transformation is found that converts the system with generalized diffusivities examined here to the simpler system considered by Toole and Georgi.

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Barry R. Ruddick

Abstract

A three-layer model is used to study the effects of pure strain flow and simple shearing flow on isolated, anticyclonic, baroclinic vortices such as Mediterranean salt lenses. Exact steady solutions are found representing elliptical vortices with uniform interior vorticity. These solutions become increasingly elliptical with increasing strain or shear, with the major axis always 45° clockwise from the principal (outflow) axis of the strain field. This is shown to be necessary so that the mean flow not exchange energy with the lens. At some Critical value of strain or shear, these solutions cease to exist. The results suggest that for a lens of a given Rossby number, there is a maximum large-scale strain beyond which the lens must undergo drastic changes in order to survive.

The geostrophic adjustment of an infinitely long strip aligned with a simple shearing flow is also investigated. It is found that the shear modifies the distance of outward adjustment, but not the profile of the adjusted region. The strong flow and vorticity near the edge, and the assumed infinite length, allow the strip to persist in environmental slim as strong as f, the Coriolis parameter.

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David Walsh and Barry Ruddick

Abstract

The influence of turbulent mixing on double-diffusively driven thermohaline interleaving is investigated. The problem is formulated using a turbulence-modified flux ratio to link the fluxes of T and S; the addition of turbulence changes the way in which the effective flux ratio varies with the density ratio R ρ. Formulation of the problem maps onto past interleaving studies, except that the flux ratio is a function of R ρ in the present work. Posing the problem in this way allows the effects of turbulence and intrinsic variations in the salt-finger flux ratio to be studied within the same theoretical framework.

Turbulence modifies the slope, wavelength, and growth rate of the fastest-growing intrusions, decreasing the range of slopes and wavenumbers that can grow. However, analysis shows that growing solutions exist for any finite value of the turbulent diffusivity Kt, suggesting that double-diffusively driven intrusions can exist in the ocean even when double-diffusive fluxes are much weaker than turbulent fluxes.

If the flux ratio is a decreasing function of R ρ (as suggested by some models of salt finger convection) a different instability occurs, which has unbounded growth rates in the high wavenumber limit (a “UV catastrophe”). In most cases, the instability can be suppressed by the addition of sufficiently strong turbulent mixing. The threshold for this instability depends upon variation of the T/S flux ratio with R ρ, and hence on the relative strengths of turbulent and double-diffusive mixing. The instability is shown to be nonintrusive in nature, as it does not rely upon lateral advection across a front; it is found to be closely related to the one-dimensional double-diffusive instability investigated by Huppert.

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David Walsh and Barry Ruddick

Abstract

The nonlinear behavior of thermohaline intrusions on a wide front is investigated using a one-dimensional numerical model. The model is used to follow the evolution of a field of intrusions from infinitesimal amplitude to a large-amplitude state characterized by inversions in temperature and salinity. It is thus possible to extend the analytical studies of Toole and Georgi and others to large amplitude, allowing for the effects of amplitude-dependent diffusivities, and for the appearance of stably stratified, diffusively stratified, and statically unstable regions in the water column as the intrusions grow.

The model runs are initialized with infinitesimal disturbances that grow exponentially in time until inversions in temperature and salinity occur. After inversions appear, the intrusions evolve toward an equilibrium state in which friction balances buoyancy forces, for both finger- and diffusive-sense basic-state stratifications. These equilibrium states are characterized by statically unstable “convecting” layers between layers of finger- and diffusively stratified fluid—the convecting layers appear when intrusions reach large amplitude and help to slow their growth. Equilibration seems to be insensitive to the specific functional forms chosen for the double-diffusive diffusivities and viscosities. The necessary condition for equilibration is that the TS flux ratio adjusts as the intrusions grow, and (within the context of the present model) turbulent mixing provides the mechanism for this adjustment.

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Barry Ruddick and Lingqi Zhang

Abstract

Stommel's two-box model of thermohaline circulation is generalized to incorporate 1) either mixed or Newtonian thermal and saline boundary conditions; 2) temperature-dependent evaporation, including a simple coupled air-sea model; and 3) a nonlinear flow law for meridional overturning. The authors prove that under steady forcing, the generalized model cannot exhibit self-driven oscillations. If the saline adjustment time is larger than the thermal, then 1) there is one and only one, stable “saline” equilibrium state corresponding to evaporation-driven sinking and 2) “thermal” equilibrium states corresponding to sinking in cooling zones may or may not exist. If they do, they come in pairs, one saddle and one stable node or spiral. A nonlinear “wiggly” flow law may lead to more than one such pair.

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William D. Smyth and Barry Ruddick

Abstract

In this paper the authors investigate the action of ambient turbulence on thermohaline interleaving using both theory and numerical calculations in combination with observations from Meddy Sharon and the Faroe Front. The highly simplified models of ambient turbulence used previously are improved upon by allowing turbulent diffusivities of momentum, heat, and salt to depend on background gradients and to evolve as the instability grows.

Previous studies have shown that ambient turbulence, at typical ocean levels, can quench the thermohaline interleaving instability on baroclinic fronts. These findings conflict with the observation that interleaving is common in baroclinic frontal zones despite ambient turbulence. Another challenge to the existing theory comes from numerical experiments showing that the Schmidt number for sheared salt fingers is much smaller than previously assumed. Use of the revised value in an interleaving calculation results in interleaving layers that are both weaker and thinner than those observed. This study aims to resolve those paradoxes.

The authors show that, when turbulence has a Prandtl number greater than unity, turbulent momentum fluxes can compensate for the reduced Schmidt number of salt fingering. Thus, ambient turbulence determines the vertical scale of interleaving. In typical oceanic interleaving structures, the observed property gradients are insufficient to predict interleaving growth at an observable level, even when improved turbulence models are used. The deficiency is small, though: gradients sharper by a few tens of percent are sufficient to support instability. The authors suggest that this is due to the efficiency of interleaving in erasing those property gradients.

A new class of mechanisms for interleaving, driven by flow-dependent fluctuations in turbulent diffusivities, is identified. The underlying mechanism is similar to the well-known Phillips layering instability; however, because of Coriolis effects, it has a well-defined vertical scale and also a tilt angle opposite to that of finger-driven interleaving.

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Trevor J. McDougall and Barry R. Ruddick

Abstract

It is shown that two methods used for eliminating the effects Of internal-wave straining on fine-scale salinity-temperature-depth profiles also eliminate finestructure in which Rp = α∂z T/β∂z S is locally constant. It is expected that finestructure indicative of double-diffusive convection will have a near-constant value of Rp and hence be suppressed (or grossly distorted) by the methods. In those few cases where vertical internal-wave advection is the only process affecting the measurements, we suggest a modification to the method of Johnson et al. (1978) which overcomes this disadvantage. When this modification cannot be applied, it is suggested that the modification developed by Joyce et al. (1978) he adopted.

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Barry Ruddick, David Walsh, and Neil Oakey

Abstract

Microstructure data from the North Atlantic Tracer Release Experiment (NATRE) are presented, providing detailed profiles of the thermal variance χ in the upper 360 m of the Canary Basin for the fall and spring seasons. The Osborn–Cox model is used to compute the diffusivity K T. The diffusivity for the depth range 240–340 m is found to be 1.0(±0.04) × 10−5 m2 s−1 in the fall and 2.2(±0.1) × 10−5 m2 s−1 in the spring, in good agreement with dye-inferred diffusivities at similar depths. Measured turbulent kinetic energy (TKE) dissipation rates were found to be contaminated by hydrodynamic noise, so the Osborn dissipation method was not used to compute K ρ. However, data segments for which the TKE dissipation rate (ε) was large enough to be unaffected by noise were used to compute the “apparent mixing efficiency” Γd. The computed Γd values are used to investigate variations in apparent mixing efficiency with respect to density ratio (R ρ) and turbulence Reynolds number [ε/(νN 2)], in an attempt to elucidate the underlying mechanisms of mixing in the NATRE region. Observed variations of Γd are compared with existing theoretical models of mixing due to: salt fingers, a combination of salt fingers and turbulence, “conventional” high Reynolds number turbulence, and low Reynolds number buoyancy-modified turbulence. Significant variations of Γd with respect to both R ρ and ε/(νN 2) are found. Although Monte Carlo tests show that some of the observed variations could be noise-induced, a substantial portion of the systematic variations the authors observed were not reproduced by Monte Carlo simulations. These trends are found to be statistically significant, and the authors conclude that they represent real variations in the apparent mixing efficiency. The authors find that Γd is an increasing function of ε/(νN 2) and a decreasing function of R ρ; these variations are not fully consistent with any of the available mixing models.

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Barry Ruddick, Ayal Anis, and Keith Thompson

Abstract

A simple technique for fitting spectra that is applicable to any problem of adjusting a theoretical spectral form to fit observations is described. All one needs is a functional form for the theoretical spectrum and an estimate for the instrumental noise spectrum. The method, based on direct application of the maximum likelihood approach, has several advantages over other fitting techniques. 1) It is unbiased in comparison with other least squares or cost function–based approaches. 2) It is insensitive to dips and wiggles in the spectrum, due to the small number of fitted parameters. It is also robust because the range of wavenumbers used in the fit is held fixed, and the built-in noise model forces the routine to ignore the spectrum as it gets down toward the noise level. 3) The method provides a theoretical estimate for error bars on the fitted Batchelor wavenumber, based on how broad or narrow the likelihood function is in the vicinity of its peak. 4) Statistical quantities that indicate how well the observed spectrum fits the theoretical form are calculated. This is extremely useful in automating analysis software, to get the computer to automatically flag “bad” fits.

The method is demonstrated using data from the Self-Contained Autonomous Microstructure Profiler (SCAMP), a free-falling temperature microstructure profiler. Maximum likelihood fits to the Batchelor spectrum are compared to the SCAMP-generated fits and other least squares techniques, and also tested against pseudodata generated by Monte Carlo techniques.

Pseudocode outlines for the spectral fit routines are given.

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